That elevated cost has nothing to do with the high-profile Autopilot crashes that have been in the headlines recently, though. Tesla crashes may be "newsworthy," but none of the publicly available crash data suggest Tesla has a statistically worse crash rate than comparable cars.

And Tesla's own internal numbers suggest that the current iteration of Autopilot actually reduced crash rates versus human drivers.

Instead, the reason for high Tesla insurance costs is something far more mundane: The bill at the body shop.

A fender-bender can cost five-figures, a number driven by the cars' aluminum construction, limited manufacturer-approved shops, and part scarcity. (Tesla isn't the only carmaker that's seeing higher repair costs due to aluminum construction - Ford's immensely popular F-150 is another example of a model seeing pricier repair bills than steel cars.)

But that could all be about to change.

At Tesla's annual meeting Tuesday, Elon Musk announced that it would start integrating Tesla-owned body shops into its service centers rather than relying on third-party shops. The decision could dramatically reduce the cost of Tesla repairs; Tesla understands that keeping insurance costs in line with peers is critical to selling vehicles long term, and having control of parts inventory, and body repair costs could go a long way in doing that.

This isn't the first time Tesla has taken steps to reduce the cost of insuring its vehicles for the road. The firm's InsureMyTesla program is an example of Tesla working directly with an insurance partner to mitigate risks and keep rates low.

But Tesla's just-announced body shop initiative is likely to have a much more dramatic impact on the cost of insurance, provided it actually results in faster, cheaper body repairs.

Meanwhile, shares of Tesla are rallying hard Wednesday on the heels of the annual meeting. From a technical standpoint, the move looks like it's lining up with a short-term and long-term bullish trend in Tesla's price trajectory.

If you're looking for an opportunity to buy Tesla, a push through $310 is the line in the sand that needs to be crossed to signal that buyers are back in control of this stock.

This article is commentary by an independent contributor. At the time of publication, the author held no positions in the stocks mentioned.